A war-weary public is willing to cut the president some slack on diplomatic initiatives. But it's not willing to do so on his domestic priorities.

The top domestic and foreign policy priorities likely to dominate the remainder of President Obama's term underscore how much the choices of even the world's most powerful person are shaped by the conditions he inherits.

The political environment Obama inherited on foreign policy is expanding his running room as he pursues a nuclear-disarmament deal with Iran, now his top international priority. Conversely, the domestic political environment that greeted Obama—and his failure to reshape it through his first term or reelection—has narrowed his margin of error for steadying his beleaguered health reform law, his top priority at home.

Obama has room to maneuver on the nuclear initiative not because Americans trust the new Iranian government, or the president's diplomatic skills, or are particularly confident that diplomacy will succeed. Obama's advantage, rather, is that the alternative has been discredited. Amid widespread disillusionment over the American military interventions in Afghanistan and Iraq, Obama is benefiting from the shattered public belief that American force can pacify the Middle East.

That's the key new element in a debate that otherwise settled quickly into familiar grooves after the agreement last weekend with Iran to curb its nuclear program in return for a temporary relaxation in economic sanctions. Since the U.S. and five other powers concluded the deal with Iran, conservative critics have besieged Obama with accusations that he is naive and weak, complete with the inevitable references to Munich and appeasement of Nazi Germany before World War II. Plenty of congressional Democrats, plus key Mideast allies such as Saudi Arabia and Israel, are leery (if not openly hostile), too.

Obama can't ignore this crossfire. But the odds remain high that he can contain it and advance negotiations long enough to test whether Iran is genuinely willing to shelve its nuclear program (a question that remains very much unanswered as longer-term talks begin). The failure of George W. Bush's attempt to transform the Middle East through American-led force has provided Obama more leeway to pursue an approach more modest in both means and ends: diplomacy that aims, in a fashion George Kennan would recognize, more to avoid the worst outcomes with Iran than to achieve the ideal.

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While polls show that Americans would ultimately use force to prevent Iran from acquiring nuclear weapons, the bipartisan congressional and public recoil against military action in Syria this fall probably offers a more revealing picture of the nation's mood after Afghanistan and Iraq. "I think from the public's standpoint, we are back to where we were in the mid-1970s [after Vietnam]," said Bill Galston, a senior fellow at the Brookings Institute. "That skepticism about overseas involvement in general and military involvement in particular is going to last for some years now." And that means most Americans are likely to give Obama a long rope on diplomacy before they conclude force is the only option left for deterring Iran.

If the public mood Obama inherited has broadened his opportunities in Iran, it has constrained him on health care. From the start, the debate over the health care law has unfolded in an atmosphere of pervasive skepticism about government. When Lyndon Johnson passed Medicare in 1965, more than three-fifths of Americans said they trusted Washington to usually do the right thing; in the decades since, scandal, war, and economic struggle steadily corroded that number, to around one in four by the time Obama passed the health reform law in 2010. (After three more years of economic stagnation and political gridlock, those numbers have fallen still further.) That's the sheer wall of skepticism, especially among whites, that Obama must scale to build support for expanding government's role in health care.

Since taking office, Obama has made the case for activist government more aggressively than Bill Clinton did. But Obama never formulated a clear strategy for rebuilding trust in Washington. On the one hand, he didn't focus as much as Clinton did on reforms (like work for welfare recipients or shrinking the federal workforce) that might reassure skeptical voters about government's capacity and efficiency. On the other, he (correctly) discarded as politically unrealistic bright-line transformative ideas such as single-payer health care or breaking up big banks. That vastly increased his chances of passing legislation but meant that even his successes (like health care and financial reform) produced programs of dizzying intricacy that require government to "thread the needle" between contending interests, as Yale University political scientist Stephen Skowronek says. "You can't mobilize around these things. They are just problem-solving."

The health law's difficulties show the vulnerabilities inherent in such precariously constructed enterprises. Obamacare's early struggles don't guarantee its collapse; it is already gaining momentum in some key blue states. But the program's troubles and complexity make it more likely to deepen than dispel public doubts about Washington. With success in Iran, Obama could solidify a shift in public opinion (from force to diplomacy) already moving toward him. But unless he stabilizes his health care plan, Obama will bequeath the next president even greater suspicion of Washington than he inherited.